The walls of hot gas conducting combustion chambers, of gas turbine plants for example, require their supporting structure to be thermally shielded against attack by hot gas. The thermal shielding can be implemented for example by means of a hot gas lining disposed in front of the actual combustion chamber wall, in the form of a ceramic heat shield for example. A hot gas lining of said kind is usually constructed from a number of ceramic heat shield elements with which the combustion chamber wall is lined over its surface area. Ceramic materials are ideally suited for constructing the hot gas lining compared with metallic materials on account of their high temperature resistance, corrosion resistance and low thermal conductivity. A ceramic heat shield is described for example in EP 0 558 540 B1. In particular a heat shield element can comprise a core zone and an edge zone, the thermal conductivity of the material in the edge zone being less than in the core zone. A heat shield element of said kind is described in EP 1 508 761 A1.